What tallit did the Rambam wear?

Usually the questions that come my way are fairly commonplace: tallit sizing, atara questions, tzitzit options, shipping time, etc. But today I got a question that really caught me off guard.

Do you know what tallit the Rambam would have worn?

The truth is I don't, but I can venture a guess. I'm pretty sure it would have been all white, because as I understand it black-striped tallits were a later development.

I say "pretty sure" because you need to keep in mind that today, a tallit is sort of a codified type of garment specifically designed for synagogue use, whereas in earlier times various cloak type garments were more commonly worn. In other words, I suspect they often resembled the clothing trends of their time period, and could easily have had some coloring.

Certainly in halacha there is room for a colored tallit:

When a garment is entirely red, green, or any other color [besides white], its white strands should be made from the same color as the garment itself. If it is green, they should be green. If it is red, they should be red.

Should the garment itself be techelet, its white strands should be made from any color other than black, for it resembles techelet. He should wind one strand of techelet around all the strands, as one does with other tzitzit that are not colored.

- Rambam, Yad, Halacha of Tzitzit, Chap. 2, Hal. 8

To get an idea of what I mean, take a look at this blog post and the link to see tallitot worn in Yemen as recently as under a century ago.